Simple Interest
Math MCQs

Question :    Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.

Correct Answer  8

Solution & Explanation

Solution

Given,

Principal (P) = $4700

Rate of Simple Interest (R) = 6% per annum

Amount (A) = $6956

Thus, time (T) = ?

Method (1) Using Formula

Calculation of Simple Interest, when Principal and Amount are given

Formual to Calculate Simple Interest when Principal and Amount are given

We know that, Amount (A) = Principal (P) + Simple Interest (SI)

⇒ Simple Interest (SI) = Amount – Principal

⇒ SI = $6956 – $4700 = $2256

Thus, Simple Interest = $2256

Calculation of the Time using forumula when Amount, Simple Interest and Principal are known

Formula to find the Time (T)

Time (T) = ^{100 × Simple Interest}/_{Principal × Rate of Interest}

⇒ T = ^{100 × SI}/_{P × R}

Thus, Time (T) = ^{100 × 2256}/_{4700 × 6}

= ²²⁵⁶⁰⁰/₂₈₂₀₀

= 8 years (using formula)

Thus, Time (T) = 8 years (from time taken before calculation)Answer

Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known

Here, we have

Principal (P) = $4700

Rate of Simple Interest (R) = 6% per annum

Simple Interest = $2256 (As calculated above by subtracting Principal from the Amount given)

We know that, interest is calculated on the basis of the Principal.

This means Simple Interest for 1 year = Rate of simple interest × Principal

Thus, Simple Interest for 1 year = 6% of Principal

= 6% of $4700

= ⁶/₁₀₀ × 4700

= ^{6 × 4700}/₁₀₀

= ²⁸²⁰⁰/₁₀₀ = 282

Thus, simple Interest for 1 year = $282

Now,

∵ If the simple Interest is $282, then the time = 1 year

∴ If the simple Interest is $1, then the time = ¹/₂₈₂ years

∴ If the simple Interest is $2256, then the time = ¹/₂₈₂ × 2256 years

= ^{1 × 2256}/₂₈₂ years

= ²²⁵⁶/₂₈₂ = 8 years

Thus, time (T) = 8 years Answer

Similar Questions

(1) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.

(2) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.

(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.

(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?

(5) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?

(6) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 4 years.

(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.

(8) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.

(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?

(10) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?